the region r is the region of the first quadrant bounded by the graph of f(x)=√x, g(x)=6-x and the x-axis. find:

(a) the area of r

(b) the volume of the solid generated when the region r is revolved about the x-axis.

(c) the volume generated when the region r is revolved about the y-axis.

i really want to understand this for other questions as well, so can you go step-by-step. : )

x = 12

y = 15

step-by-step explanation:

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.

answer: the answer is 110